School

Carleton UniversityDepartment

Mechanical EngineeringCourse Code

MECH 3700Professor

Andrew SpeirsStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**2 pages of the document.**CASTING

STRESS, STRAIN, AND DEFORMATION

Hollomon’s Equation:

linear region only

RA: reduction in area

uniform elongation (before onset of necking)

useful up to fracture

true strain as a function of engineering strain

true stress

material properties:

engineering strain at the onset of necking

true stress at the onset of necking

engineering stress at the onset of necking

Fick’s Second Law:

General Solution:

Evaluate using the Gaussian error function:

Temperature Gradient in a mold:

Fick’s First Law evaluated at the mold-cast

interface (x=0):

PRIMARY MANUFACTURING

- four basic raw materials in making pig iron &

functions: iron ore; coke –fuel; limestone-combines

impurities; hot air-burn coke; use blast furnace

- conversion furnaces: Bessemer-oxygen used to

oxidize carbon and other impurities, oxides form slag

on surface, lime may be added, high N from air can

cause embrittlement; open hearth-air and iron oxides

provide oxygen to oxidize carbon and other

impurities, oxides form slag on surface, limestone

added to control composition of flux to remove

impurities, can produce scrap metal, burns oil, long

cycle, higher quality steel than Bessemer; basic

oxygen (most common)- charged with scrap and

molten iron, oxygen blown into furnace in water-

cooled lance (20 min.), flux (lime) controls slag to

remove impurities, oxygen removes carbon through

intermediate iron oxide product, higher quality than

open hearth; electric arc- oxidation by O2; removes

impurities by slag; electric heat expensive; produces

very high quality steel; Bayer-a mix of ground bauxite

and complex chemical rxns (2NaOH + bauxite →

Na2O∙Al2O3+4H2O+red mud); Hall-Héroult-alumina

converted to Al in electrolytic cells containing cryolite,

Al is deposited on cathode and tapped, cast into ingots

Casting poured at the melting temperature:

OR rate of heat transfer:

BULK DEFORMATION

Dry interface:

Thickness of fluid layer:

N: force required to move body along die

F: normal force

: average interface frictional stress

P: normal pressure, often die pressure applied

: material shear strength (temp. dependant)

: effective coefficient of friction

highest effective coefficient of sticking friction is 0.5

:

: shear strength of absorbed surface film

average friction of the area of direct and mediated contact

: lubricant velocity

: entrance velocity

: angle of entry

: stress required for forming

`Heat flux is the heat transfer per unit area:

For a temperature, , above the melting

temperature:

S: solidification distance

2.1 Identify two products that you think were made using (a) ingot casting, (b) continuous casting and (c) shape casting. Discuss the reasons for your selections. 2.2

State one advantage and one disadvantage of each of the shape casting techniques described in this chapter. 2.3 Identify the causes of porosity in metal castings.

Explain briefly how each type can be minimized. 2.4 Briefly outline the mechanism responsible for the formation of dendrites in casting a pure metal. Why is dendritic

structure disadvantageous? 2.5 If you sectioned a cast part, you are likely to observe voids within the casting. Explain how you would distinguish between solidification

porosity and gas porosity in terms of the void shape and location. 2.6 The tapered plate shown is to be cast in sand using the horizontal riser/sprue. Explain the

cause of the centreline shrinkage at the location shown. Explain the cause of the centreline shrinkage. Sketch an improved riser/sprue arrangement so that shrinkage in

the tapered plate is avoided. 2.7 (a) Using data from Table 2.3, plot the temperature profile in a large sand mould containing an aluminium casting 5 min after pouring.

(Assume a 1-D conduction heat flow model and a pouring temperature equal to the melting temperature.) (b) Calculate the heat flux flowing from this casting 5 min

after pouring. (c) Calculate the growth rate of the solid-liquid interface 5 min after pouring. (d) Calculate the total thickness solidified after 5 min. 2.8 (a) A very large

iron plate of thickness 100 mm is cast by pouring iron at its melting temperature into a sand mould, such that heat is withdrawn from both faces of the solidifying plate.

Estimate by calculation the time for the plate to solidify if the initial mould temperature is 25 °C. (b) Because in part (a) the iron is cast at its melting point, the liquid

iron sometimes begins to solidify prior to filling the entire mould. To solve this problem the iron is heated to 60 °C above its melting temperature prior to pouring.

Calculate the new solidification time if the initial mould temperature is 25 °C. 2.9 A 10 cm high cylindrical riser is positioned on top of a 10 cm3 cube casting. The riser

extends from the top face of the cube through to the surface of the mould, as illustrated. Assume no heat is lost through the top of the riser to the atmosphere. An

insulator is placed around the riser which effectively doubles the cooling time. Estimate (by calculation) the diameter of the cylindrical riser required to prevent

macroporosity. 2.10 A cylindrical casting is 0.1 m in diameter and 0.5 m in length. Another casting of the same material is elliptical in cross-section, with major axis

twice the length of the minor axis, and has the same cross-sectional area and length as the cylindrical casting. Both pieces are cast using the same conditions. What is the

ratio of the solidification time of the elliptical casting to the solidification time of the circular casting? The perimeter P and area K of an ellipse are:

. 2.11 What are the advantages and disadvantages of using eutectic alloys for shape casting? 2.12 From an Al-Si diagram, you are considering

making a shape casting from two alloys, one containing 2% Si, and the other containing 12% Si. Of these two alloys: (a) which will be more prone to coring, (b) which

will be easier to feed, and (c) which will be more prone to microporosity? 2.13 Why should metals be cooled to a temperature as low as possible prior to casting? 2.14

Calculate the relative amount of H2 absorbed in molten Al cast in an atmosphere where the partial pressure of H2 is atm, compared to the amount of H2 absorbed in

molten Al in a vacuum where the partial pressure of H2 is atm. 2.15 The max. eq’m solubility of H2 at a partial pressure of 1 atm in liquid Mg is per 100 g.

This drops to per 100 g upon solidification. The density of Mg (liquid and solid) is

. (a) What would be the gas porosity

of the Mg casting if liquid

saturated with H2 at 1 atm were allowed to solidify? (b) What partial pressure of H2 should be maintained over the melt if a pore free casting is required? 2.16 How

does the form of carbon in cast iron influence brittleness of cast iron parts? How is the form of carbon in cast iron parts altered to control these properties? 3.1 During

stress-strain tensions tests, many engineering materials exhibit a decrease in engineering stress prior to final fracture. However, the true stress increases continuously

until final fracture occurs. Explain this apparent anomaly. 3.2 A metal has an elongation to failure of 25% and a reduction of area of 50%. Did this metal neck when

tested in uniaxial tension? Support your answer by calculation and explanation. 3.3 During a tensile test of a round metal specimen with an initial diameter of 12.8mm, a

maximum load of 53.4 kN is reached. At this load the cross sectional area is 60% of the starting initial area. Calculate the mean true flow stress of the metal during this

deformation. 3.4 (a) A metal specimen with a cross-sectional area of 5 cm2 is pulled in tension. The UTS is 250 MPa and the cross sectional area corresponding to the

UTS is 4 cm2. Find K and n. (b) If a piece of this metal that is 5 cm wide and 20 m long is deformed, in a drawing manufacturing process, from a thickness of 2 cm to 1.8

cm, what is the ideal work of deformation? (c) Does the calculation of part (b) under- or overestimate the work required for deformation? (d) After the deformation

of part (b), estimate the yield strength of the metal. 3.5 A cylinder of material is compressed at a constant strain rate of from a starting height of 1 cm to a

height of 0.3 cm. What is the time required for the compression? 3.6 A uniaxial tensile test is performed and the UTS is measured to be 28 ksi. When true stress is

plotted against true strain on logarithmic scales, the experimenter calculates that the strength constant is 50 ksi and the strain hardening exponent is 0.25.

Determine the accuracy of the calculated values. 3.7 True strain can be defined as either

or

. With the aid of a typical engineering stress-

engineering strain curve, illustrate the domain for which each of the true strain definitions is not applicable. Give reasons for your answer. 3.8 A fully annealed bar is

deformed from a diameter of 5 mm to a diameter of 4 mm, causing working hardening so that the yield strength of the bar after deformation is 490 MPa. The bar is

then further deformed to a diameter of 3 mm and more work hardening occurs, increasing the yield strength to 603 MPa. The bar is then fully annealed at the 3mm

diameter and the deformed to a diameter of 2 mm. Calculate the yield strength of the bar at the 2 mm diameter. Assume (a) that the strain during deformation does not

exceed the true strain to fracture, and (b) the plastic deformation of the bar obeys the Hollomon equation. 3.9 The initial diameter of a tensile specimen is 10 mm. After

a certain load is applied the diameter is reduced to 8 mm. Calculate the engineering strain and true strain when the diameter is 8 mm. State any assumptions. 3.10 A

metal bar has initial dimensions of 76 mm in length, 12.7 mm width and 7..6 mm thickness. After a load is applied a student measures the new dimensions as 89mm

length, 11.9 mm width and 7.1 mm thickness. Comment on the accuracy of the measurements of the deformed bar. 3.11 A specimen of 10 mm diameter is tensile tested

and a maximum load of 5 kN recorded with a corresponding 20% reduction in the cross-sectional area. A second specimen of the same material is loaded to a true

strain of n/2 (where n is the stress exponent). What load is applied to the second specimen? 3.12 A cylinder is compressed at a constant strain rate of . What is

the time required to compress the cylinder to two-thirds of its original height? What will be the time required to compress the cylinder to one-third of the original

height? 3.13 During a high temperature tensile test of a material, it is noted that changing the strain rate by a factor of 10 increases the true stress by a factor of 3. Is

the material superplastic? Support your answer by calculation. 3.14 A cylinder of 10 cm height and 5 cm2 initial cross-sectional area is hot compressed with a force of 5

kN, the die-workpiece interface is lubricated with boron nitride, which is very effective at reducing friction, and therefore friction effects can be ignored. The hot

deformation equation for the metal of the cylinder is MPa. Calculate the cylinder height after the force is applied (

). 3.15 (a) A metal conforms to

the hot deformation relationship

MPa where

is expressed in . A rod of this material 30 cm long and 1 cm2 cross-sectional area is oriented

vertically, fixed at its upper end and a mass of 10 kg attached to the lower end. Assuming homogenous deformation (and negligible changes in cross-sectional area),

calculate the length of the rod 1 h after loading. (b) From the information provided in part (a), is the deformation behaviour of this material superplastic? State a reason

for your answer. (c) List the four conditions usually necessary for superplastic deformation to occur. 3.16 A 5 cm long, 1.28 cm diameter rod of high strength aluminium

is tested in tension to failure. The yield strength and UTS were found to be 345 MPa and 485 MPa, respectively, and the total elongation to failure is 18%. (a) Calculate

the load at yielding and the load at the ultimate tensile strength. (b) Assuming that necking occurs when the specimen has elongated uniformly by 15%, what is the

instantaneous diameter at the onset of necking? (c) What is the true stress at the onset of necking? (d) What are the values of n and K for the Hollomon equation? 4.1

Identify two advantages of hot working versus the cold working of metals. 4.2 A cylinder () is compressed by an open die forging process. The

true strain to fracture the cylinder is and the governing deformation relationship is MPa. The lubricant provides a friction coefficient of 0.1. The

process is limited by either platen yielding or fracture. If the yielding stress of the platens is 800 MPa, do the platens yield of does the specimen fracture?

Heat transfer during continuous casting:

Estimate solidification time:

Sand casting sprue:

Gas porosity (Sievert’s Law):

macroporosity-liquid shrinkage, solidification

shrinkage, solid shrinkage, low fluidity;

microporosity-decreased strength and fatigue life,

trapped within dendrite growth, trapped liquid

solidifies and shrinks, shrinkage volume must be filled

by more liquid (requires low viscosity to flow through

dendritic structures, viscosity of liquid near melting

temperature, and thus in mushy zones, tends to be

very high, micropores form as a result, change alloy to

reduce mushy zone, increased temperature gradients

also reduce size of mushy zone and promote

nucleation, avoid long, thin sections, faster liquid

shears dendrites; gas porosity-gases more soluble in

liquid than in solid (mostly H2), sudden decrease in H2

solubility from solidification causes formation of H2

bubbles in interior, spherical

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